Modded SAT Question Bank
by Abdullah Mallik dedicated to DPT SAT Batches and Someone Special | GitHub
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Test
Math
Domain
Advanced Math
Skill
Nonlinear equations in one variable and systems of equations in two variables
Difficulty
Hard
ID: f65288e8
Modded SAT Question Bank by Abdullah Mallik

the fraction with numerator 1, and denominator x squared, plus 10 x, plus 25, end fraction, equals 4

If x is a solution to the given equation, which of the following is a possible value of x plus 5 ?

  1. one half

  2. five halves

  3. nine halves

  4. eleven halves

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Correct Answer: A
Rationale

Choice A is correct. The given equation can be rewritten as the fraction 1 over, open parenthesis, x plus 5, close parenthesis, squared, end fraction, equals 4. Multiplying both sides of this equation by open parenthesis, x plus 5, close parenthesis, squared yields 1 equals, 4 times, open parenthesis, x plus 5, close parenthesis, squared. Dividing both sides of this equation by 4 yields one fourth equals, open parenthesis, x plus 5, close parenthesis, squared. Taking the square root of both sides of this equation yields one half equals, x plus 5 or negative one half equals, x plus 5. Therefore, a possible value of x plus 5 is one half.
Choices B, C, and D are incorrect and may result from computational or conceptual errors.

Question Difficulty: Hard
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